Logic machine.



LOGIC MACHINE.

c. P. R. MACAULAY.

APPLIATION PILBIUULY 18,1910.

COLUMBIA PLANouRAPH Co..wAsH|NaTON. n.12,

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LOGIC MACHINE.

APPLICATION FILED JULP 18,1910.

1,079,504, Patented Nov. 25, 1913.

l 4DSHEETSSHEET 2.

LOGIC MACHINE.

C. P. R. MACAULAY.

APPLICATION 'FILED JULY 18,1910.

coLuMBlA PLANOGRAIH co..wASHlNGTON, D. C.

C. P. R. MACULAY.

LOGIC MACHINE.

APPLICATION FILED JULY 18,1910.

- Patented Nov. 25, 1913.

4 SHEETS-SHEET 4.

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coLuMnlA PLANooRAPH Co..wAsHlNnToN. 0.1:.

entran srarns rarest onirica errantes P. R. MAQAULAY, or cHIcAGo, rnmrrcrsf` LOGIC IVILACI-IINE.Y p'

My invention relates to logic machines in which movable elements are employed toV difl'erentiate groups of characters, denoting terms of propositions, so as to exhibit logical operations; andthe objects of my invention are, first, to provide means for inanipulating such elements by subjecting. them to an operating influence and by restricting the operation of such influence on certain ofv such elements; and second, to provideV means for disclosing the relation of propo-- sit-ions ofthe same logical. import.

shall explain my invention more fully by reference to the accompanying Vdrawings, Showing the preferred embodiment thereof, in which- Figure l is a plan view of the machine, parts being broken away to reveal interior mechanism, other interior mechanism and certain marks thereon being shown in dotted lines; Fig. 2 is a: plan view with the cover removed to show interior mechanism, certain marks on such internal mechanism being omitted for the sake of clearness andA certain movable parts beingshown in positions different from the positions ofsuch parts in Fig. l; F Sis a sectional elevation on line 3 3 of Fig. 2 with the cover in place;,Fig. 4 is a sectional elevation on line 4 4 of Fig. 2 with the cover in place; Fig. 5 is a sectional elevation on line 5 5 of Fig. 2 with the cover in place; Fig. 6 is a sectional elevation on line 6 6 of Fig. 2 with the cover in place; Fig. 7 is aplan view in section of certain internal mechanism on line 7 7 of Fig. 8; Fig. 8 is a sectional elevation on line 8 8 of Fig. 2 with the cover in place. y

Like parts are indicated by similar characters of reference throughout the different figures.

A box or casing cz', ofV any suitable material, serves to support and protect the mechanism. Sixteen character strips b rest on rigidly fixed supports c. These characterv Speciicatoniof Letters Patent.\` v

A.its third position.

strips are maintainedV iny parallel positionsatented-Nov. 25,1913'. Y appneationniea511137184910.' seriaiNof'srzso. l i' and are' preferably separated ,slight-lys by",`

vsmall pins dj projecting from the-supports, vbut they .normally have free Vlongitudinal movement within certain limits,` yThe-se lon-` gitudinal, movements of the different character strips are accomplished-by*tilting themachine through a` suiicient angle either away from or toward theoperator, according: to the `direction in whichit is desired to have` the strips move, all,V strips free to move sliding on their. supports c. The position-ofY the machine when tiltedaway from the operator will be referred to as its rst position, its horizontal positionV will be referred. t'o as its secondposition, and its position when tiltedi'toward the operator as I preferably rely on gravity for `the movements of the character strips b" when the machine is placedV in either its first or third position, but l do not wish to be limited'to this agency. On the upper face of each character strip Z/ appear three groups of characters, as shown in Fig. 1,` one groupnear each end and another nearV the center ofthe strip. The uppermost group consists of a dash, a ,starr and a certain combination of characters distinctive of the character strip; the middle group consists of a dash, the'same combinationl of characters and astar; the third group consists of the same combination of4` characters and. two dashes,4 Suitable openings e through the cover lof the casing are so positioned as to reveal one or another of the` three parts of each group of characters on eachcharacter strip. When a character strip isin its first position, the combination of characters belonging tothe uppermost group, the star ofthe middle'group and the lowermost dashof the third groupof characterson'the character strip are re- 4' vealed through the coverof the machine.

lVhen the character strip is its second position, the star of theuppermost group, the combination ofVK characters ofthe middie group and al dash of the lowermost group of characters are revealed. When the character stripis in-its third position, the dash of the uppermost, the4 dash of the middle and the combination of characters of the lowermost group are'revealed` in Fig. lthe character strips areshoWn in various positions. `Counting from the left,`

the irst, second,fiifth andsixthare shown?? in their rst. positions;.the tenth,` eleventh n' and fourteenth, vare shown their second positions; thev third, fourtlnlseventh, eighth,

ninth, twelfth, thirteenth, 'fifteenth and ysixteenth are shown in their third positions. These' are' the three positionsvwhich charfacter strips may assume in this form of the machine.V The combinations of characters, Y inv this form of thev machine, are combinations of small and Ycapital letters of the al- Yphabet;"The combinations shown, from left tov right Vare as follows: abcd, Abcd, aBcd,

i ond strip Vthe by one .orvrmo're ofthe letters marked on them. vThus the Abad strip is the'sec- 125D strips are the ninth f and thirteenth; the Ac strips are the secondyfourth, tenth and twelfth; the"A strips are the second, fourth, sixth, eighth, tenth, twelfth, fourteenth and sixteenth strips. It will be observed that a capital and small form of theV same letter never -appear on the same character strip, and

that either the capital or the small form of each letter appears on every strip.

' i The longitudinal movement of each char- "acter strip Zi is restricted by suitably lomined, being the first position of the Y character strip, above referred to; and,

similarly, the lowermost or third position of each character strip b is determinedv by another pin so located as to be interceptedl in its downward mQoveinent'by the lower, support c. The intermediate or second position of the character strip is determined in a manner hereinafter described.' Various other pins f, as well as those above mentioned, normally have free Y passage through open spaces g in the top "edges ofeiglit slides h and a ninth slide o,

adapted to move close below and crosswise ofthechaiacterstrips b. These slides L aresupported and guided by openings in the'left hand sidefof the casingra and in `the support Vz' near the right handV side of the casing.. Their eXtreme movement toward the left is limited by the'vstriking of stops It', which project upwardly from their e right hand ends and Yare intercepted by the y support c'. Their eXtreme movement-.toward the right is limited by theYV striking of said Y Y stops't against thebar k, which is free to moveto the right until it strikes the stops Z.

`This bar 7c isY maintained parallel to the f v'character strips b by means ofconnecting links m. VThe slides/hare adapted 'to be movedindividually to their extreme right hand positions by pressing on their left hand ends, which protrude through openings inthe left hand side of the casing a so as to be accessible. rIhey are adapted t0 be moved simultaneously to their extreme left hand positions by pressing on the projection 7c of the parallel bar 7c, said projection 7: protruding through an opening in the right hand side of the casing af so as to be accessible. Then a slide 7L is in its extreme left hand position, it is said to be in its first position, and when it is in its extreme right hand position, it is said to be in its second position.

On the cover of the vmachine a and on the left hand side thereof are certain letters adapt-ed to identify the slides L, as shown in Fig. 1. The first or uppermost slide is called subject a slide or predi cate A slide the second slide is called subject A slide or predicate a slide; the third, subject b slide or predicate B slide, etc.

In Fig. 3 is shown a sectional elevation of the first or uppermost slide (called subject a slide). In Fig. 5 is shown a sectional elevation of the eighth slide (subject D slide). In Fig. 4t is shown a sectional elevation of the fifth slide (subject c slide). The second, third, fourth, sixth and seventh slides 7i have projections n and open -spaces g arranged in a manner similar to that in which the projections n and open spaces g of the fifth slide are arranged.

The parts described are so relatively arranged that when the slides 7L are in their first positions', their open spaces g will be in alinement with the pins f of the character strips, thereby permitting free longitudinal movement of the character strips b', but when any one of the slides 71, is pressed into its second position, its projections n will intercept pins f of those eight of the character strips that have combinations of characters marked thereon that do not contain the subject letter of the slide 71, that may be pressed into its second position, (or to state the matter otherwise, those character strips that have combinations of characters that do contain the predicate letter of the slide a, that is pressed into its second position)-which will be readily seen on comparing Figs. l and 2. Thus, if the third slide (subject b slide, or as it may also be called, predicate B slide) is pressed into its second position, a pin f of the third, fourth, seventh, eighth, eleventh, twelfth, fifteenth and sixteenth character strips b will. be intercepted to prevent movementof said character strips from their first positions, and these character strips are the aBcd, ABccl, /LBCCL ABCd, aBcD, ABCD, @BCD and ABCD character strips, none of which contains the subject letter b of the slide pressed. and all of which contain the predicate letcontaining the subject letter b of said ,slidev and have no pins f thatv can be intercepted by the projections of the subject bslide.

`if two slides are pressed, one being the subject small form of any letter andthe other being the subject large form of the same letter, say, subject and subject B, and the machine is put into its thirdposition,-there will be no movement of the character strips, because the first of thesev two slides `will lock in the first position all the character strips that do not contain the small form of the letter (that is all those that do contain the large form of the letter) and the second ofthe two slides will lock in the first position all the character strips that do not contain the large form of the letter (that is all those thatdo contain the small form of the letter), and as every character strip contains either the small or the large form of every letter, it follows that all the character strips will be locked in the first position.

lf two or more slides are pressed, no two of which are the subject small formand the subject large form of the same letter, say, subject A, subject Z), subject C and subject l slides, and the machine is then put into its third position, it is obvious that the character strips that do not contain A, and vthose that do not contain Z), and those that do not contain C and those that do not contain al (that is all those that contain a, B, c or D) are locked in the first position, and the character strip that contains A, Z), C and CZ,

that is the ACcZ character strip is the only one not locked and it falls to the third position. It will now be seen that when slides are pressed and the machine is put into its third position, those character strips that contain combinations of characters which contain all the subject letters of the slides pressed, fall into the third position, and the character stripsthat contain any one or more of the predicate letters of the slides pressed remain in the first position;

provided, however, that no two of' the slides press-ed are the subject small form and subject large form of the same letter.

A ninth slide 0, having projections n, and

open spaces g similar to those of the slidesf 7L, has an extreme left hand position in which its open spaces are in alinement withV the pins f' and an eXtreme righthand'position in which its projections are in alinement with the pins The eXtreme left hand position of the slide o is called itsfiirst position and is determined by its shoulder o coming in contact with the left hand end of the casing a and its eXtreme right hand position, called its second position,A is determined by its shoulder o2 coming in contact with the support z'. The distance belconsistent row ofy openings.

vtween any two slides L is substantially equal to Vthe extreme longitudinal travel of the character strips b, as above described; the projections n, however, of the slide o` are at substantially ivefninths of the above men tioned distance below the lowermostrslide It.

When the slide 0 is in its first position,

the, character strips may f all from the lirst to the third position, or vice versa, because their lowermost pins f pass 'throughthe open -spaces of the slide 0, but when the slide `0` 1s pressed 4into its second position, then character stripsfalling from thei'irst towardl the third position are arrested in the sec- ,ond position, because their lowermost pegs f `strike the projections?? of the slide o; and,

character strips are obstructed in their move-V ment by the project-ions n ofthe slide 0. The slide o may bev restored from its second to its first position by pressure on that part of it that protrudes from the right of the casing a so as to be accessible.

The chief purpose of the slide 0 is to Y enable the operator to select certain combinations from those appearing in the con sistent row of openings and to cause them to appear in the special row of openings for inspection and then to restore them to the Suppose that combinations containing C are, with others,

in the consistent row of openings, and it is desired to examine the combinations containin C. The slide o is pressed intofits secon position and subject fC' slide is pressed, and the machine is put into its third position. All the combinations containing C (the subject letter of ythe slide pressed) that were in the'consistent row of openings vwill disappear therefrom (their places being taken by stars to denote that the absence of such combinations is only temporary) and those combinations will appear in the special row of openings. These combinations having been inspected, the machine is put into its rst position, whereupon the combinations disappear from the special and reappear in the consistent openings. If the projection 7c is now pressed, the subject `C slide will be restored to its Vfirst position.

A plan vieT of the slide 0 and of the two letter slides above it, is shown in Fig. 7. The various marks on the character strips are not shown in Fig. 2, in order that the positions of the pegs f on the several strips may be the more easily seen. On the cover of the machine a (Fig. l), the letter X identifies the slide 0 where it protrudes from right of the machine, and-the letter Z identifies the projection 7c of the parallel bai' k rWhere it.protrudesfrom the right of the machine.

f lAn operation called rectifying the machine, consists in pressing the keys Y and Z, placing the machine into vthe first and then into vits second position (horizontal). The result offthis operation is to cause the slide 0 and Vall the slides 7L and'all the cha-racter strips o toassume their firstpositions.

`The machine when so constructed1 canv be used'f in the investigation of logical inferences and in the analysis of propositions.

The method of using the machine for such purposes Will depend upon the nature of e the-matter under investigation, and l shall proceedV to #sho-iv how Ythe machine may be used in certain' eases, by Way of illustration.

- The capital letters A, B, C, and VD may be used to denote the positive aspectsof terms -of propositions, and the small letters a., b, c,

andd may be used to denote the negative aspects kof said-terms, respectively. So that if, for instance, A is taken to denote gold,

Vthen a, `Will denote Whatever is not gold..

The letters maybe made to denote not only things, but also qualities, the truth of propositions, or any circumstances Whatever. A combination of letters on any character strip denotes the possibility of combining the things, qualities, etc., that may be represented by the letters of the combination. Thus if A denotes gold and B denotes metal, then the combination AB denotesthat it is possible that some gold is metal,or it is Vpossible tliat'some metal is gold;V the combination Ab denotes that it is possible that some gold is not metal, or that it is possible that something that is not metal is gold; the combinationY aB denotes that itis possible A that, something that is not gold is metal, or 45.

that some metal is possibly no-t gold; the combination ab denotes that it is possible that something that is not gold is not metal, or that it is possible that something that is not metal is not gold. In the same manner significance may be given tocombinations of three or four letters. rllie combinations appearing in the openings marked Consistent denote circumstances that are possin ble, and when combinations appear in the openingsmarked lnconsistent, they denote circumstances that are impossible. Combinations in the openings marked Special are combinations selected from the consistent combinations.

When all the character strips are in their first positions, the combinations of characters shown-in the consistent openings denote all'combinations of the four terms, A, B, C and D and their negatives that can possibly occur. If but three terms are involved in the matter under investigation, the D character strips, the last eight, can be eliminated by pressing subject D slide, putting machine into its third and then back to its second position and pressing the key Z. The effect of this operation is to retain in the first position the d character strips, the first eight, and to cause the VD character strips, the last eight, to move to their third position. Thereafter the character al, ap-

nearing in the first ei 0fht character combinations may be disregarded, and those eight combinations will be all the combinations of the three terms, A, B and C and their negatives that can possibly occur. Similarly, if but tivo terms are involved in the matter under investigation, after eliininating the D combinations, as above, the C coinbinations (the fifth, sixth, seventh and eighth) remaining in the first position, may be eliminated by pressing subject C slide, putt-ing the machine into its third and then back into its second position and pressing the key Z. All the C, as Well as the D combinations will then be in the inconsistent position, and the only combinations remaining in the first or consistent position will be the first four, and those four will be all the combinations of the tivo terms A and B and their negatives that can possibly occur and the characters c and d appearing in the first four combinations may thereafter be disregarded.

A'universal proposition is impressed on the machine by pressing appropriate slides, While the machine is in its second (horizontal) position, then putting the machine into its third position, (whereupon the character strips that bear combinations that denote What is impossible, untrue, etc. move to their third positions), then returning the machine to its second position and pressing the key Z, the effect of pressing the key Z being to restore to their first positions the slides that were pressed.

Subject letters of slides pressed are deemed connected by the conjnnctive and, While predicate letters of slides pressed are deemed connected by the disjunctive or.

Universal propositions may be stated in different forms and the manner of impressing propositions of representative types will now be explained.

A proposition stating that a certain combination o-f terms is impossible is impressed on the machine by pressing slides the subject letters of which form the combination alleged to be impossible. Thus, to impress on the machine the proposition, V'Vhatever is A and B and 0 (not C) is impossible, the slides to be pressed are the second, fourth and fifth, the subject letters of which are respectively A, B and c. vThen the ma ing all the subject characters` of slidesv pressed will, as above explained, move to their third positions, and, therefore, in this case the AB@ character strips move to their third positions, as required by the proposition.

A proposition stating that no combination of characters is possible unless it contains one or others of certain characters, or inother l Words, that every possible combination of;

characters must contain one or others of cer.-

tain characters, is impressed on the machine by pressing slides the` predicate characters of which are the characters the presence of one or more of which is alleged `to be necessary. Thus, to impressV on the machine the proposition Everything is a (not A) or b (not B) or C, the slides tobe pressed arel the second, fourt-h and fifth, the predicate letters of Which are respectively,a, b and C. When the machine is put into its third positio-n, the character strips that bear combinai.

tions containing any one or more of the predicate letters of slides pressed, Will, as above explained, be retained in their iirst positions, and, therefore, in this case, all the character strips that bear combinations of characters containing a, b or C Will remain in their first positions, signifying that allI sition of this paragraph is of the same logical import as the proposition of the preceding paragraph.

ATo impress a proposition Vof the form A is C the slides to be pressed are the second, the subject letter of which is A, (that being the subject of the proposition) and thelifth slide, the predicate character of which is C, '(that being the predicate of the proposition). The subject letters of these tvvo slides being A and c, the A0 combinations, Which are inconsistent vvith the proposition, move to their third positions. Similarly, to impress a proposition such as, A is b .(not B), the slides to be pressed are the second, the subject letter of Which is A, and the fourth, the predicate letter of Which is b.' The subject letters of these two slides are A and B, and, therefore, Vthe character strips bearing combinations containing both A and B, being inconsistent with this proposition, move to their third positions.

A proposition of the form Whatever A and B is C is impressed on the machine by pressing the second slide, the subject letteiof which is A, Tand the fourth slide, the subject letter. of'vvhich is B and the fifth slide, the j predicate letter of Which is C. The subject letters of the three slides being A, B and c, the ABG characterstrips, Which f denote inconsistent cases, will move to their third positions When themachine is put into its third position. v

A Vproposition of the form, A is B or yC is impressed o-n the machine by pressing the second slide, the subject'letter of which is A, andthe third slide, `the predicate letter of Which is B, and the fifth slide, the .predicate letter of which is C. The subject letters/of the `three slides being A, b and @,the Abc combinations, which are inconsistent with the proposition, Y move to rtheir third positions, when the machine is put into its third position.

A proposition of the form Whatever is Aand is C or D, is impressed` on the machine by pressing the second slide, the subject letter oflwhich is A, and the fourth slide, the subject letter of which is, B, and the fifth slide, the predicate letter of which is C, and the seventh slide, the predicate letter of which is D. The subject letters of the four slides Vpressed are A, B, c, and d, and, thereforethe ABccZ combination, Which is inconsistent With the proposition, vvill, when `the machine is` put into its third position, .move to `its third or inconsistent position.

Auniversal proposition that cannot be i vstatedin one or other of the above forms,

Willon investigation be found to be a combination of one or more propositions, each of which is capable of being stated in one or other of such forms. Compound propositions of this kind are impressed on the ma-` chine by impressing successively the `propositionsjof Which they are composed Thus,`

the proposition, A is identical with B, means A is B and B is A. The proposition, A is B and C, means A is B and A is'C. The proposition, A is B o-r C, but not both means, A is B or C, and A is ZJ (not B) or c (not C). The proposition,A or B, Whichever is considered, is

C, means`A is C and B is C. Com? pound propositions of other types may similarly be reduced to two or more propositions, each offWhich' `in effect asserts that some combination of characters is impossible, and

may be impressed `on'the machine as above.

shovvn. I. Particular propositions in effect assert that some combination of characters, appearing in the consistent openings, denote `cases that `are not `merely possible, but are true.V To

impress a particular proposition on the machine, the `key X` (the projecting part of the slide oV onl the .left hand side of the machine) is pressed and then slides are pressed, the subjectletters of which denote the fterms,

'both of the subject and of the predicate, of the particular proposition, and then the :machine is put into its third position, whereupon the combinations asserted by the proposition to be true will be caused to appear in the special openings." Thus, toimpress on the machine the proposition, Some A is B, press the key X and the second slide, the subject letter of which is A, and the fourth slide, the subject letter of which is B, and

then put the machine vinto its third position.

The character strips that bear combinations V that contain'both A and B, that is the AB character strips are the only ones that can move from the first position, but they cannot reach the third position, because their lowermost pegs f are intercepted by the projec- 'tions of the slide 0, and said character strips are therefore arrested in the second position, and the AB combinations will appear in the special openings. The AZ) combinations (denoting thatV some A may be not B)r and the aB combinations, (denoting that some B VVmay vbe not A) remain with others in the sistent withA all the propositions.

' may be not B) does not appearin the consistent openings shows that that combination cannot be true. Again, if it is observed, forV instance, that the combination AB always occurs with C, but in one case combined with D and in-v another case combined with d, the inference may be drawn that whatever is A `and B is C, but may be D or not D. Y

The examination of the consistent combinations may be facilitated by pressing the key X and then the slide, the subject letter of which is the character in regard to which it is desired to draw inferences and then putting the machine into its third position. All the'combinations that are in the consistent vopenings thatcontain that letter will then appear in the special openings. When they have been inspected, the machine is put into its first positions, whereupon the said com- Y binat-ions will return to the consistent openings. 1f it' is desired to assertain what inferences may be drawn in regard to a combination of characters, the slides, the subject letters of which form the .combination are pressed, and when the machine is put into its third positions, the character strips bearing not.

yspecial openings.

that combination of cliaractei's will move to the second position, and the combinations will appear in the special openings.

Vhen, one of a series of propositions is a particular proposition, the particular proposition is impressed on the machine last.

Suppose the following problem: Four hunters, A, B, C and D, occupied a camp in different ways for seven days. (1) On days when A hunted B did not. (2) On days when B hunted, D also hunted, but C did (3) On days when D hunted, A or B hunted. How did they dispose themselves during the week? On how many days did D hunt and with whom? Y Let A denote any day on which A hunted and let a denote any day on which he did not hunt. Let similar meanings be given to the other letters. The proposition marked (2 is equivalent to the two propositions: (2a

When B hunted, D hunted, and (2") when B hunted C did not. The propositions may be stated symbolically thus: (l) A is b. (2a) B is D. (2b) B is c. (3) D is A or B. Bectify the machine. (1) Press subject A and predicate Z) slides; put machine into the third and then into the second position and then press the key Z. (2a) Press subject B and predicate D slides; put machine into the third and then into the second position and press Z. (2") Press subject B and predicate c; put machine into the third and then into the second position and press Z. (3) Press subject D and predicate A and predicate B slides; put machine into the third and then` into the second position and press Z. The

following combinations remain in the consistent openings j abcd-showing that on one day none of them hunted.

Abad-showing that on one day A hunted alone.

abCd-showing that on one day C alone hunted. f

AbCiis-showing that on one day A and C hunted and B and D dld Abclg-showing that on one day A and D hunted and B aud C did aBcI-showing that on one day B and D hunted and A and C did no AbCD-showing that on one day A, C and D limited and B did not.

The combinations denoting cases in which D hunted may be selected from the others and caused to appear in the special openings by pressing the key X and subject D slide and putting the machine into the third position. The combinations containing D, that is, AbcD, aBcD, and ACD, appear in the (The appearance of the machine at this point is shown in Fig. 1). It is apparent that D hunted on three days as shown in these combinations.

The sets of characters used to identify the slides protruding fromthe left side of the machine, may also be usefully employed to disclose propositions having the same logical import as agiven proposition. As shown above, a proposition is impressed on the machine by pressing certain of the slides. When the slides are pressed, they may be read in various ways, according to the characters used to identify the slides, and thus propositions of the same logical import may be discovered. Thus, in order to impress on the machine vthe proposition, A case Where A and D are present, is a case Where B or C is present, the slides to be pressed are the second, the subject letter of which is A; the eighth, the subject letter of Which is D; the third, the predicate letter of Which is B; and the fifth, the predicate letter of which is C. The subject letters of these slides are respectively: A, D, t, c. The predicate lett/ers of the slides are respectively: a', d, B, C. Any one or more of the slides pressed may now be taken as subject slides, and the rest, if any, of the slides pressed may be taken as predicate slides, or all the slides pressed may be taken as subject slides, or all of them may be taken as predicate slides. In the present case, if all the slides are taken as subject slides We have the proposition, A case Where A and D are present and B and C are absent, is impossible. If all the slides are taken as predicate slides, We have the proposition, in every case A is absent, or D is absent, or B is present, or C is present, or, if for instance, We taken subject D and subject c and predicate t and predicateB, We form the proposition, A case Where D is present and C absent, is a case Where is absent or B is present. Upon consideration it Will be seen that if the original proposition be true, then these others (and more thatV may be formed in a similar manner)Y must also be true.

lWhile l have herein shown and particularly described the preferred embodiment of my invention, l do not Wish to be limitedxto the precise details of construction shown,v

as changes may readily be made Without departing from the spirit of my invention, but,

Having thus `described myinvention, l claim as new and d-esireto secure by Letters Patent the following:

l. A plurality of characterstrips each having symbols thereupon to represent terms of propositions; a casing in Which these character strips are slidably mounted and in which the character strips are free to be moved in opposite directions by the force of gravity acting thereupon When the casing is suitably tilted; and means for restricting movement of selected character strips While permitting other character strips to slide When the casing is tilted, said casing having openings therein at each of which a symbol appears and which symbols are changed by manipulation of the casing to cause the character strips to slide.

2. A plurality of character strips each having symbols 'thereupon' to represent terms of propositions; a casing in which these characterstrips are slidably mounted and in Which the character strips are free to be movedrin opposite directions by the force of gravity acting thereupon when the casing'is suitably tilted; means'i'or restricting movement of selected character strips While permitting other character strips to slide when the casing is tilted, said casing having 'openings therein at each of which a symbol appears and Which symbols are changed by manipulation ofthe casing to cause the character strips to slide; and means for differentiating groups of character strips and the symbols borne thereby.

i 3. A device for exhibiting logicaloperations, including'.` a pluralityV of movably mounted character strips carrying symbols lrelated in pairsgfmeans for restricting the movements of said character strips to eiect ditferent combinations of said symbols, each combination containing one, vbut not both, of the members of every pair of related symbols; and means for applying, collectively,

to "the character strips carrying combina-V tions containing any given symbol, restrictions against operation.

4l. lIn a device for ascertaining propositions of the same logical import, a plurality of movably mounted characterstrips carry- 4ingfa series of symbols related in' pairs; a

second plurality of movably mounted chariacter strips carrying a second series of the same symbols, in which each symbol of the lirst series is transposed with its related symbol; meansl for applying restrictions against operation to'character strips and a table formed of the tWo series, so that each synibol-.ofone series is collocated With its related symbol in the other series.

V*In Witness whereof,V I' hereunto subscribe my name this fourteenth day of July A. D., 1910.

CHARLES P. n. MACAULAY.

Witnesses:

G. L. GRAGG, j Griso. C. DAvIsoN.

Copies of this patent may be obtained for ve cents each, by addressing the Commissioner of Patents,

Washington, D. G. 

